Automated centerline extraction method and generation of corresponding analytical expression and use thereof

ABSTRACT

A computer implemented method ( 350 ) for determining a centerline of a three-dimensional tubular structure is described. The method includes providing an edge-detected data set of voxels that characterize a boundary of the tubular structure according to a three-dimensional voxel data set for the tubular structure ( 360 ). A gradient field of a distance transformation is computed for the edge-detected dataset ( 380 ). A voxel data set corresponding to a centerline of the tubular structure is computed according to derivative of gradient field ( 390 ).

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 61/029,934, which was filed on Feb. 20, 2008, andentitled AUTOMATED CENTERLINE EXTRACTION METHOD AND GENERATION OFCORRESPONDING ANALYTICAL EXPRESSION, and claims the benefit of U.S.Provisional Patent Application No. 60/932,213, which was filed on May30, 2007 and entitled AUTOMATED CENTERLINE EXTRACTION METHOD ANDGENERATION OF CORRESPONDING ANALYTICAL EXPRESSION, both of whichapplications are incorporated herein by reference.

TECHNICAL FIELD

The present invention relates generally to image processing and, moreparticularly, to a method and system to extract a centerline of anobject, such as three-dimension tubular structure.

BACKGROUND

Anatomical information can be obtained through the use of a variety ofimaging modalities, such as computed tomography (CT), computed axialtomography (CAT), and magnetic resonance imaging (MRI). These and otherimaging modalities obtain substantial amounts of imaging datacorresponding to numerous slices through a region of a patient's body.The imaging data can allows for construction of a three-dimensionalvolumetric data set representing the various structures in a given areaof a patient's body subject to the scan. Existing techniques can beutilized for rendering a two- or three-dimensional volume of theanatomical structures, such that arbitrary points or regions of interestcan be viewed. The information from the scans can thus be analyzed aspart of a diagnosis to determine an appropriate course of treatment.

One particular application of such imaging data is to examine tubularinternal body structures, such as the aorta, colon, and the like, forprocedural planning purposes. The planning can include preparation forrepair or reconstruction of such structures. An integral part of suchplanning typically involves a determination of sizing and geometry ofinternal tubular structures based on the imaging data acquired for agiven patient. Currently, sizing of many support structures (e.g.,vascular endografts) is a labor-intensive process with the potential tobe error-prone. For instance, many existing measurement techniques, tendto be imprecise, are frequently difficult to reproduce, and require agreat amount of user interaction. Another weakness of many existingapproaches is that there is no analytical definition of the geometry andtopology of the patient's anatomy. Many advances have occurred in imageanalysis; however, these advances have generally permitted theapplication of endovascular repair to more complex anatomy rather thansimplifying the process.

As an example, a proper sizing requires a skilled operator to use asophisticated imaging workstation for making all the necessarymeasurements. The results of many existing approaches thus depend,largely, on the judgment and care of the user and, thus, may vary fromapplication to application. Existing methods measure the vasculardiameters in the acquired 2D slices. However, the orientation of theseslices is not necessarily orthogonal to the tube-like structure undermeasurement. This limitation can cause inaccurate diameter and lengthmeasurements.

SUMMARY

The present invention relates generally to image processing and, moreparticularly, to a method and system to extract a centerline of anobject, such as three-dimension tubular structure. The extractedcenterline can be utilized to generate an analytical expression for thecenterline, based on which ah analytical expression can be determinedfor a surface of the tubular structure.

One aspect of the present invention provides a computer implementedmethod for determining a centerline of a three-dimensional tubularstructure. The method includes providing an edge-detected data set ofvoxels that characterize a boundary of the tubular structure accordingto a three-dimensional voxel data set for the tubular structure. Agradient field of a distance transformation is computed for theedge-detected dataset. A voxel data set corresponding to the centerlineof the tubular structure is computed according to derivative of thegradient field.

Another aspect of the present invention may provide an image processingsystem. The system can include a distance transform programmed tocompute a distance transformation for an edge detected data set, theedge detected data set including voxels that represent athree-dimensional volume that includes a structure of interest. Agradient operator is programmed to compute a gradient vector field ofthe distance transformation. A centerline extractor is programmed toidentify a voxel data set corresponding to a centerline of the structureof interest based on the gradient vector field. As an example, aderivative of the gradient vector field can be computed, such that thecenterline extractor identifies the centerline based on the derivativeof the gradient vector field.

The analytical expression can be used to design an implantable devicethat is dimensioned and configured according to the analyticalexpression. Additionally or alternatively, the analytical expression canbe fused with another image, such as can be used intraoperatively. Theshape of an elongated device (e.g., a steerable catheter) can bedetermined as a function of the analytical expression, whichdetermination can be utilized to configure and guide the elongateddevice to a desired anatomical position in a patient.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an example of an image processing system that can beimplemented according to an aspect of the invention;

FIG. 2 depicts an example of a segmented image that can be generatedaccording to an aspect of the invention.

FIG. 3 depicts a graphical example of part of an edge-detected data setthat can be computed according to an aspect of the invention.

FIG. 4 depicts a graphical example of a distance transform that can becomputed for part of a voxel data set according to an aspect of theinvention.

FIG. 5 depicts a graphical example of a distance transform gradient thatcan be determined for the distance transformation of FIG. 4 according toan aspect of the invention.

FIG. 6 depicts a graphical example resulting from performing aderivative of the distance transform gradient of FIG. 5 according to anaspect of the invention.

FIG. 7 depicts an example representation of part of a voxel data setillustrating part of a centerline identified from the derivative of FIG.6.

FIG. 8 depicts an example of a centerline of an arterial lumen mat canbe identified in accordance with an aspect of the invention.

FIG. 9 depicts an example of an analytical centerline overlaid on asegmented image of an arterial lumen according to an aspect of theinvention.

FIG. 10 depicts a graphical example of analytically-fit centerlines foran aorta and branch vessels that can be generated according to an aspectof the invention.

FIG. 11 depicts an example of a portion of a centerline with periodictangent lines drawn along the centerline according to an aspect of theinvention.

FIG. 12 depicts an example of apportion of a centerline and localcoordinate axes distributed along the centerline according to an aspectof the invention.

FIG. 13 is a graphical illustration of a centerline and centerlineslices that can be employed for surface fitting according to an aspectof the invention.

FIG. 14 depicts an example of a three-dimensional surface rendering andcenterline for a portion of an arterial lumen according to an aspect ofthe invention.

FIG. 15 is an example computer system depicting an example operatingenvironment that can be used for implementing systems and methodsaccording to an aspect of the invention.

FIG. 16 depicts an example of a graphical user interface that can beutilized to obtain sizing and geometry information for arterial lumenaccording to an aspect of the invention.

FIG. 17 is a flow diagram illustrating an example method that can beimplemented for extracting a centerline and generating a surface modelaccording to an aspect of the invention.

FIG. 18 depicts an example of a system that can be utilized to fuse amodel into another image cording to an aspect of the invention.

FIG. 19 depicts an example of an image of a patient's anatomydemonstrating anatomical landmarks.

FIG. 20 depicts an example of an image demonstrating anatomicallandmarks associated with a representation of a surface model accordingto an aspect of the invention.

FIG. 21 depicts an example of an image acquired for a patient, such asduring an intraoperative procedure.

FIG. 22 depicts an example of a fused image demonstrating arepresentation of a surface model superimposed on the acquired image ofFIG. 21 according to an aspect of the invention.

FIG. 23 depicts example of a system that can be utilized to control asteerable medical device according to an aspect of the invention.

FIG. 24 depicts an example of ah analytical centerline and surface for atubular anatomical structure demonstrating a trajectory betweencenterlines of adjacent branches that can be determined according to anaspect of the invention.

DETAILED DESCRIPTION

The present invention relates generally to an automated centerlineextraction process that can be utilized to ascertain an analytical modelor expression that describes the geometry of a curved path. As oneexample, the curved path may correspond to an anatomical tubularstructure, such as including an arterial lumen (e.g., the aorta) andassociated branches. The centerline extraction process includescomputing a gradient field of a distance transformation determined foran edge-detected image dataset for a given tubular structure. The vectorgradient field can be differentiated (e.g., using a scalar derivative)to identify a voxel data set that forms the centerline of the structure.The centerline voxel data set can be utilized to generate an analyticalexpression of the lumen's centerline, such as a spline (e.g., abasis-spline) model. The spline model (or other analytical expression)of the centerline can be used, in conjunction with previously acquiredsegmented image data for the structure, to generate a correspondinganalytical expression for the entire surface of the lumen. The approachdescribed herein can be employed to automate the generation of complexendovascular graft planning data as well as to facilitate repair of avariety of anatomical structures. For instance, the resulting analyticalexpression for the centerline and the surface of the lumen can providean accurate representation of the anatomical structure applicable in avariety of diagnostic techniques and methods. Additionally oralternatively, the analytical expression can be fused with anotherimage, such as can be used intraoperatively. The shape of an elongateddevice (e.g., a steerable catheter) can be determined as a function ofthe analytical expression, which determination can be utilized toconfigure and guide the elongated device along a path to a desiredanatomical position in a patient. An implantable device can also bedimensioned and configured as a function of the analytical expression.

As will be appreciated by those skilled in the art, portions of theinvention may be embodied as a method, data processing system, orcomputer program product. Accordingly, these portions of die presentinvention may take the form of an entirely hardware embodiment, anentirely software embodiment, or an embodiment combining software andhardware. Furthermore, portions of the invention may be a computerprogram product on a computer-usable, storage medium having computerreadable program code on the medium. Any suitable computer-readablemedium may be utilized including, but not limited to, static and dynamicstorage devices, hard disks, optical storage devices, flash memorydevices, and magnetic storage devices.

Certain embodiments of the invention are described herein with referenceto flowchart illustrations of methods, systems, and computer program,products. It will be understood that blocks of the illustrations, andcombinations of blocks in the illustrations, can be implemented bycomputer-executable instructions. These computer-executable instructionsmay be provided to one or more processor of a general purpose computer,special purpose computer or workstation, or other programmable dataprocessing apparatus (or a combination of devices and circuits) toproduce a machine, such that the instructions, which execute via theprocessor, implement the functions specified in the block or blocks.

These computer-executable instructions may also be stored incomputer-readable memory that can direct a computer or otherprogrammable data processing apparatus to function in a particularmanner, such that the instructions stored in the computer-readablememory result in an article of manufacture including instructions whichimplement the function specified in the flowchart block or blocks. Thecomputer program instructions may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational steps to be performed on the computer or other programmableapparatus to produce a computer implemented process such that theinstructions which execute on the computer or other programmableapparatus provide steps for implementing the functions specified in theflowchart block or blocks.

FIG. 1 depicts an example of an image processing system 100 that can beutilized to identify a centerline of a tubular structure. The system 100can also be employed to generate an analytical expression or centerlinemodel based on the identified centerline. The system further cangenerate a corresponding surface model that parameterizes the surface ofthe tubular structure based on the centerline model.

The system 100 employs raw image data 102 such as may be obtained bycomputed axial tomography (CAT) or computed tomography (CT). Theapproach described herein relates to post-processing of the image, data102, such that different techniques and equipment can be utilized toacquire the image data. Those skilled in the art will understand andappreciate various types of scanners that can be utilized to acquire theimage data 102, including CT scans, magnetic resonance imaging (MRI) orother 3D imaging modalities. The scan or a series of scans can beperformed over a portion of a patient's body that includes an anatomicalstructure of interest to provide the image data 102.

As one example, the image data 102 can include a native voxel data setfor a region of interest and a contrast voxel data set for the sameregion. The respective voxel data sets can be acquired for a givenpatient at different times. For instance, the contrast voxel data setcan be acquired after injecting the patient with a contrast material,such as an x-ray die. As a result of the scans occurring at differenttimes, the coordinates of the structures in the respective scans may notcorrespond directly to each other. Such mismatch may be due to externalmovement of the patient, internal movement of the patient's organs ormovement of the scanner's sensing array.

For sake of simplicity of explanation, much of the remaining discussionis described in relation to image data that includes a tubularanatomical structure in the form of an arterial lumen; namely, the aortaand its associated branches. It will be further appreciated that theapproach described herein is not limited to any particular anatomicalstructure as the approach is generally applicable to any generallytubular structure that may be considered to have a centerline and anexterior. The tubular structure can include one or more branches, eachof which can follow a complex or tortuous curved path. The approachdescribed herein can also be implemented to generate an analyticalexpression for tubular structures that may be moveable between differentorientations as may occur over a period of time. Stated differently, theimage data 102 can correspond to a series of scans, such as may beconsidered 4D scans (e.g., a 3D CAT scan including a temporaldimension), for which one of more analytical expressions can begenerated.

The system 100 includes an image preprocessor 104 that is programmedand/or configured to perform predetermined pre-processing on the imagedata 102. In the example of FIG. 1, the preprocessor 104 includes aregistration block 106 and a segmentation block 108. The registrationblock 106 can include methods and operations programmed to register thecontrast and native image sets to each other so that the correspondencebetween points in voxels in the respective data sets are known. As oneexample, the registration block can employ a maximization algorithm,such as in which a registration quality of a particular pair of datasets in the respective images can be determined. For example, thecloseness of the match between data sets A(x, y, z) and B(x, y, z) canbe identified by a quality factor Q, which can be expressed as follows:

$\begin{matrix}{Q = {\sum\limits_{x,y,z}\sqrt{{A(x)}{B(x)}}}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$The registration block 106 thus can employ metrics to reward peaks thatmatch other peaks and as well as to indirectly penalize valleys that donot match other valleys. A search algorithm may be employed to identifywhich of the values maximizes the quality function Q. A correspondingtranslated data set can then be generated.

The preprocessor 104 can also include a segmentation block that can beprogrammed to segment or separate the desired anatomical structure fromthe rest of the image set. As one example, a segmentation process mayutilize intensity cropping, intersecting data-sets and computingconnected components. The segmentation process can be partially or fullyautomatic process. The intensity cropping can be employed as apreliminary part of the segmentation process by cropping the imageaccording to intensity. The intensity cropping procedure can beperformed on both input data sets—the native voxel data set and thecontrast voxel data set. As a further example, upper and lower intensitybounds can be defined by the user to provide real time feedbackcommensurate with the results of the cropping operation.

Because intensity cropping individually may not sufficiently segment thevolume of interest from the remaining image data, segmentation blockfurther may include a method for intersecting the volumes of the twoimage data sets. For instance, the intersecting can be implemented bytaking the intensity-cropped arterial scan and removing voxels notpresent in the intensity-cropped native scan. The remaining datarepresents a volume closer to the isolated arterial lumen. Thesegmentation process may further include computing a connectedcomponent. As one example, a neighbor relation can be defined on thevoxel set, which relation can be utilized to isolate connectedcomponents. For the example of an arterial lumen, the connectedcomponent will contain closely isolated arterial lumen with fewdistractions. An example of a segmented arterial lumen is depicted inFIG. 2, indicated at 110.

The system 100 may further include an edge detection method 114. Theedge detection method 114 is programmed to identify voxels at theborders of the volume in the segmented image data provided by the imagepreprocessor 104. The edge detection method 114 generates anedge-detected data set that identifies the voxels at the border of thetubular structure. The voxels at the border of the lumen, as containedin the edge detected data set, identify contours that characterize theshape of the tubular structure.

Those skilled in the art will understand and appreciate variousedge-detection algorithms that have been developed, which can beutilized for providing the edge-detected data set. Examples of edgedetection methods 114 may range from relatively simple threshold withspatial derivative to more complex iterative procedures that includederivations based on statistical analysis. However, it will beappreciated that in many cases the segmented image data for anatomicaltubular structures, such as arterial lumens and colons, are sufficientlystructured such that simpler edge detection may be sufficient. Forinstance, the edge-detection method 114 can be employed to mark voxelsat the borders of the segmented tubular structure, such as by iteratingover each voxels neighbor in the segmented data set for the tubularstructure. If any voxel is not within the tubular structure or lumen, itis marked as a border. Such an efficient process can be performed inlinear time. An example of a graphical representation of an edgedetected data set for a given slice of the segmented image is depictedin FIG. 3, as indicated at 116.

The system 100 also includes a distance transformation 120 that isprogrammed to compute a distance transform for the edge-detected dataset provided by the edge detection block 114. For example, with theedge-detected data set defining the border or edge of the tubularstructure, the distance transformation 120 can apply a metric toidentify the distance each image element or voxel is from a nearestfeature or voxel in the border. The distance transformation 120 canconvert the edge detected data set from a binary or Boolean image (FIG.3) into a corresponding gray-level image (FIG. 4), in which the valuesassociated with each of the voxels corresponds to its distance from itsnearest border feature. Alternatively, the distance transform can endowthe edge-detected data set with an additional field representing thecomputed distance information. For the example of a tubular structure,the resulting distance transform can be a three-dimensional distancetransform (DT). As a further example, the distance transformation 120can generate the three-dimensional DT as a scalar field that satisfiesthe Eikonal equation:|∇DT|=1  Eq. 2with the boundary conditions:B(i,j,k)=

=DT(i,j,k)=0.Those skilled in the art will understand and appreciate various distancemetrics that can be utilized by the distance transformation 120 toprovide a corresponding distance transform of the edge detected-dataset. For example, the distance transformation 120 can be programmed toemploy a Manhattan distance metric, a Euclidean distance metric, aChebyshev distance metric or other distance metrics that may be known oryet to be developed.

FIG. 4 depicts an example graphical representation of a distancetransform, indicated at 122, in which the distance transform has beensuperimposed over the edge detected data set of FIG. 3. The values ofthe image elements correspond to the distance values determined by thedistance transformation 120. The representation of the distancetransform depicts zeroes at the boundary of the structure, with thevalues increasing smoothly as one moves away from the boundary.

Referring back to FIG. 1, the system 100 also includes a gradientoperator 124 that is programmed to compute a gradient field of thedistance transform generated by the distance transformation 120. The 3-Dderivative resulting from the gradient operation represents how thefield is changing with respect to the linear dimensions. A mathematicaldefinition of the gradient operator 124 can be expressed in Cartesiancoordinates for 3-D scalar space as follows:

$\begin{matrix}{{\nabla F} = {{\frac{\delta\; F}{\delta\; x}\hat{x}} + {\frac{\delta\; F}{\delta\; y}\hat{y}} + {\frac{\delta\; F}{\delta\; z}\hat{z}}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

-   -   where F corresponds to the scalar distance transform.

Those skilled in the art will understand and appreciate that thegradient operator 124 typically is a continuous function. Due to thediscrete nature of the data being processed and in order to maintainsymmetry, the 3-D gradient of the scalar distance transform can beapproximated as follows:∇F(i,j,k)≈(F(i+1,j,k)−F(l,j,k){circumflex over(x)}+(F(i,j+1,K)−F(i,j−1,k))ŷ+(F(i,j,k+1)−F(i,j,k−1)){circumflex over(z)}  Eq. 4The gradient operator 124 thus generates a corresponding distancetransform vector gradient field for the scalar distance transform.Because of the highly structured form of the distance transformation,the gradient yields a unit vector for each voxel.

An example of a corresponding distance transform vector gradient field,indicated at 126, is depicted in FIG. 5. As shown in FIG. 5, for everyvoxel inside the boundary of the structure, the resulting vector fieldpoints towards the centerline. Because, the vector gradient field alwayspoints towards the centerline, the direction of the vector gradientchanges rapidly at the centerline. The system 100 also includes aderivative block 128 programmed to quantify this change in direction.The derivative block 128 computes a derivative of the gradient vectorfield provided by the gradient operator 124. The derivative block 128computes the derivative by differentiating the gradient vector fieldprovided by the gradient operator 124. The resulting derivative providesa measure of how the gradient vector field changes, which facilitatesextracting the centerline.

As one example, the derivative block 128 can be programmed to compute ascalar derivative of the gradient vector field. While such an approach(computing a scalar derivative of a vector field) may be consideredmathematically peculiar, the scalar derivative of the vector fieldenables identification of voxels (by a centerline identification block132) according to where the gradient of the distance transform changesrapidly. The scalar derivative, for example, can be computed usingneighborwise dot products. As described herein, the gradient vectorfield is highly structured since the distance transformation satisfiesthe Eikonal equation as discussed above (see, e.g., Eq. 2). The highlystructured nature of the gradient vector field results in neighboringvectors that differ only in direction. Consequently the derivativecomputation need only detect a rapid change in direction in the vectorfield to identify which voxels correspond to the centerline.

By way of further example, when looking at a particular slice of imagedata, such as the distance transform gradient of FIG. 5, the derivativecomputation can be implemented by performing the neighborwise dotproduct of a given voxel (or image element) relative to the top, bottom,left and right neighboring voxels. Alternatively or additionally,diagonal neighbors can be utilized as part of the neighborwise dotproduct computation for computing the scalar derivative.

FIG. 6 depicts a gray scale image representation of the scalarderivative, indicated at 130, computed for the gradient vector field ofFIG. 5. Since the computed derivative provides a measure of relativechange in direction, the centerline can be identified as including a setof one or more contiguous voxels having the highest values. In theexample of FIG. 6, the centerline of the structure corresponds to thewhite area near the center.

For automated centerline identification, the system 100 can include acenterline identification block 132 that is programmed to identify thecenterlines based on the derivative of the gradient vector field. Forexample, the centerline identification block 132 can be programmed toperform thresholding or other characterizations on the scalar derivativefield. The thresholding further may be followed by a Boolean subtractionof the borders, to provide an accurate reconstruction of the centerlineof the tubular structure. The identified centerline thus can be providedas a voxel data set for subsequent analysis.

FIG. 7 depicts an example a graphical representation 134 of anidentified centerline 136 overlaid on a corresponding edge-detectedimage for part of a tubular structure (e.g., the border has not beensubtracted out). The set of one or more voxels that define thecenterline thus can be identified in the segmented data (from the imagepre processor 104) to provide a voxel data set corresponding to thecenterline for a plurality of scan slices acquired for the tubularstructure. FIG. 8 depicts graphical representation 138 of a centerlinefor an arterial lumen (e.g., the descending aorta), such as can bestored as a voxel data set (e.g., in the form of a voxel array).

The identified centerline can be utilized as a part of furtherprocessing to determine the complete geometry of the tubular structure,including its surface and associated branches. The system 100 thusincludes a centerline model generator 140 that is programmed to derivean analytical expression (or model) corresponding to the centerline. Asdescribed herein, the analytical expression for the extracted centerlinefurther can be processed to compute an analytical expression for thesurface based on the segmented data and the analytical expression forthe centerline.

As an example, the centerline model generator 140 is programmed toproduce an analytical expression of the centerline based on the voxeldata set generated by the centerline identification block. It will beunderstood that the resulting centerline image may not exhibit isthinness, but may be more than one voxel thick. This characteristic thusis considered when deriving the analytical expression for thecenterline.

By way of further example, the centerline model generator 140 canperform a “marching” procedure. The procedure begins at one end (e.g.,corresponding to a top or proximal end) of the tubular structure anditerate-downwards, using a flood-fill type of algorithm. Because of thehighly structured narrow form of the centerline voxel dataset, thecenterline model generator 140 reliably iterates along the axis of thetubular structure, and accurately determines the geometric properties ofthe centerline. The algorithm can be visualized as a propagating wavefront. The wave front begins in the topmost slice and, at everyiteration, propagates along the centerline, maintaining a cohesivestructure. A split of the advancing wave front into more than oneconnected-subcomponent occurs at the point where the centerline splitsdue to a branch. This predictable behavior of the marching procedurefurther can be exploited to extract the geometric knots, such as may beidentified at periodically occurring locations along the centerline. Thedistance between such knots may be a tunable parameter. Thecenter-of-mass of the marching wave front can be monitored and thecenter-of-mass can be periodically recorded as defining a correspondinggeometric knot. If the wave front divides, the largest portion isretained as corresponding to the main branch and the remaining connectedsubcomponents begin new branches.

The centerline model generator 140 can produce a spline model (e.g., abasis or B-spline model) of the centerline as a function of theextracted geometric knots. By way of further example, the centerlinemodel generator 140 can use uniform cubic B-splines to represent thecenterline geometry of the tubular structure. For instance, a splineinversion algorithm allows a spline curve to be fit to thecenters-of-mass that is recorded in the marching process. An example ofan analytical centerline 144 is shown in FIG. 9 overlaid on the originaldata from the intensity-cropped, arterial scan, indicated at 142. Theanalytical centerline that is produced by the centerline model generator140 according to an aspect of the invention provides a good basis forthe construction of an accurate analytical surface model for the tubularstructure.

As described herein, the tubular structure can include one or morebranches. Each branch of the tubular structure can represented as aseparate list of recorded centers-of-mass, forming a separate set ofgeometric knots for each branch. To ensure that the centerline of theentire tubular structure is representative of the correct geometry, thecenterlines of each branch should form a single continuous structurewithout gaps. To achieve such continuity, the centerline of childbranches can be “stitched” to the centerline of their parent branches bya performing an association procedure. As one example, the centerline ofeach child branch (except for the first or main branch) can be given oneadditional geometric knot placed ahead of the rest. This additional knotcan be selected from the parent's centroid list such that both the slopeand knot spacing of the branch are preserved as much as possible. Thesecontradictory requirements can be balanced against one another using anempirically determined regularization parameter.

FIG. 10 depicts an example of a graphical representation of a centerline146 that can be defined by an analytical expression for an arteriallumen. In the example of FIG. 10, the centerline includes a main branch148 and a plurality of child branches 150. Each branch 148 and 150further includes geometric knots, such as can be determined through amarching process described herein. The spacing between adjacent knotsalong the centerline can be a tunable parameter.

Returning to FIG. 1, a surface model generator 160 is programmed tocompute a surface model 162 corresponding to an analyticalrepresentation of the surface of the tubular structure based on theanalytical expression of the centerline. The surface model generator 160can perform a surface fitting procedure that leverages the accurateanalytical centerline to compute an analytical surface appropriate forthe topology of the lumen. Since the approach described herein producesan accurate analytical centerline model, the accuracy of the resultingsurface model 162 can be high relative many existing approaches. Such asurface model can be of great utility in applications involvingvisualization, simulation, and prosthetic design. For example, theanalytical surface model 162 can be utilized by standard engineering andanalysis tools, such as computer aided drawings tools, finite elementanalysis and the like.

The surface model 162 can also be converted into a corresponding imagerepresentation that can be utilized by an imaging system, such as may bepart of an intraoperative imaging (e.g., angio) system or an imageprocessing system running as instructions on a PC or workstation. Thiscan be implemented, for example, by exporting the analytical surfacemodel 162 as a numerical representation in a desired format to definethe three-dimensional surface model. The numerical representation can beconverted to an appropriate image representation in a suitable formatfor graphical display (e.g., as a wire frame or mesh). The resultingimage derived from the model can be registered with or superimposed ontoanother image for analysis and evaluation. Thus, the model can begenerated, converted into an appropriate format of image data, such asto enable use in real time intraoperative procedures.

The surface fitting procedure can compute mathematical expressions thatrepresent each branch of the tubular structure as a lofted B-splinesurface. The surface, for example, is defined by a series oftwo-dimensional slices, each encoded as a periodic B-spline. Each of theslices can be computed by constructing local aligned coordinate systemsat key points periodically placed along the centerline. The spacingbetween adjacent points along the centerline can be tunable parameter.The key points, for example, can correspond to the geometric knots ofthe centerline defined by the centerline model or the spacing betweensuch points can be determined independently of the knots determined forthe centerline model.

FIG. 11 depicts representation of a centerline 170, such as can bederived as described herein. Tangent lines 172 are determined for thekey points along the centerline 170. The spacing between points alongthe centerline shown in FIG. 11 is for simplification of illustration,as a tighter spacing between adjacent points typically is employed toimprove accuracy of the resulting surface model 162.

In FIG. 12, local coordinate systems 176 are shown at the key pointsalong the centerline 170. The local coordinate systems 176 are depictedas two-dimensional Cartesian coordinate systems orthogonal to respectivetangent lines 172. It will be appreciated that the angular differencebetween the tangential lines in adjacent slices corresponds to therelative amount of curvature between the points at which the tangentiallines are located. The local coordinate systems 176 can be arrangedrelative to each other using a common clock system in which the origin(e.g., midnight) in each local coordinate system is the same in allslices. Each local coordinate system thus defines a two-dimensionalslice that is utilized to drive a marching algorithm that locates thesurface boundary relative to the points along the centerline. Theboundaries of each slice can be determined based on the data produced bythe image pre-processor 104, such as corresponding to segmented imagedata. For instance, the algorithm marches radially outward from thecenterline of the lumen until it reaches an edge or border of thesegmented volume. The boundary between the final internal voxel and thefirst external voxel is then marked as a geometric knot corresponding toa point along the boundary of the surface. A plurality of such geometricknots are determined to represent the surface geometry at each slice.

FIG. 13 depicts a graphical illustration of a plurality of centerlineslices 180 extending through selected key points 182 along a centerline184 of a generally tubular structure 186, such as the aorta. FIG. 13also depicts an enlarged partial view of a slice 180 taken through thecenterline and a set of corresponding geometric knots 188 determined(e.g., by a marching procedure) for the surface of the tubular structure186.

The computed slices define a lofted surface. To construct arepresentation of the entire surface, an interpolation can be performedbetween these slices, such as by using nonperiodic B-spline functions.The interpolation process can be similar to the process used within eachcross-sectional slice. For example, inverse spline algorithm can beemployed to derive appropriate control geometry to achieve adequateinterpolation. FIG. 14 depicts a graphical representation of an examplesurface model 190 that can be generated for a multi-branched tubularstructure (e.g., a portion of a patient's descending aorta). In FIG. 14,a corresponding centerline 192 for the tubular structure is also shown.

To evaluate the lofted surface, each point on each cross-sectional slicecan be treated as a geometric knot on a longitudinal curve. One suchlongitudinal curve exists for every value of the section curves'parameter u. The longitudinal curve is one dimensional in terms of itsparameter v, resulting in a two-dimensional surface indexed by these twoparameters.

FIG. 15 illustrates an example of a computer system 200 that can beemployed to execute one or more embodiments of the invention employingcomputer executable instructions. Computer system 200 can be implementedon one or more general purpose networked computer systems, embeddedcomputer systems, routers, switches, server devices, client devices,various intermediate devices/nodes or stand alone computer systems.Additionally, computer system 200 can be implemented on various mobileclients such as, for example, a cell phone, personal digital assistant(PDA), laptop computer, pager, and the like.

Computer system 200 includes processing unit 201, system memory 202, andsystem bus 203 that couples various system components, including thesystem memory, to processing unit 201. Dual microprocessors and othermulti-processor architectures also can be used as processing unit 201.System bus 203 may be any of several types of bus structure including amemory bus or memory controller, a peripheral bus, and a local bus usingany of a variety of bus architectures. System memory 202 includes readonly memory (ROM) 204 and random access memory (RAM) 205. A basicinput/output system (BIOS) 206 can reside in ROM 204 containing thebasic routines that help to transfer information among elements withincomputer system 200.

Computer system 200 can include a hard disk drive 207, magnetic diskdrive 208, e.g., to read from or write to removable disk 209, and anoptical disk drive 210, e.g., for reading CD-ROM disk 211 or to readfrom or write to other optical media. Hard disk drive 207, magnetic diskdrive 208, and optical disk drive 210 are connected to system bus 203 bya hard disk drive interface 212, a magnetic disk drive interface 213,and an optical drive interface 214, respectively. The drives and theirassociated computer-readable media provide nonvolatile storage of data,data structures, and computer-executable instructions for computersystem 200. Although the description of computer-readable media aboverefers to a hard disk, a removable magnetic disk and a CD, other typesof media that are readable by a computer, such as magnetic cassettes,flash memory cards, digital video disks and the like, in a variety offorms, may also be used in the operating environment, further, any suchmedia may contain computer-executable instructions for implementing oneor more parts of the present invention.

A number of program modules may be stored in drives and RAM 205,including operating system 215, one or more application programs 216,other program modules 217, and program data 218. The applicationprograms and program data can include functions and methods programmedto implement centerline extraction such as described herein. Theapplication programs 216 can also be programmed to compute an analyticalexpression for the centerline as well as an analytical expression forthe surface of the tubular structure. Additional application programscan be employed to evaluate the resulting surface model based on theteachings contained herein.

A user may enter commands and information into computer system 200through one or more input devices 220, such as a pointing device (e.g.,a mouse, touch screen), keyboard, microphone, joystick, game pad,scanner, and the like. These and other input devices 220 are oftenconnected to processing unit 201 through a corresponding port interface222 that is coupled to the system bus, but may be connected by otherinterfaces, such as a parallel port, serial port, or universal serialbus (USB). One or more output devices 224 (e.g., display, a monitor,printer, projector, or other, type of displaying device) is alsoconnected to system bus 203 via interface 226, such as a video adapter.

As an example, FIG. 16 shows part of a display 300 that can be utilizedto perform analysis of a tubular structure. In FIG. 16, the display 300includes a graphical representation 302 of a tubular structure. In theexample of FIG. 16, the representation 302 includes a surface of anaorta 304 and the centerline 306 of the aorta, such as can be renderedfrom analytical expressions (or models) generated based on the teachingscontained herein. The graphical display 300 can be implemented as partof a graphical user interface that can be employed to facilitatedetermining geometry and dimensions of a portion of a tubular anatomicalstructure. For instance, a user can employ the input device 220 (e.g., amouse or other pointing device) to mark points 308 and 310 along thecenterline. Because centerline 306 as well as the shapes of the aorta304 and associated branch vessels are described as a series ofmathematical equations and parameters, the locations and distancesneeded for sizing can be calculated and provided to the user. Forexample, a separate dialog box 314 can be rendered on part of thedisplay 300. The dialog box 314 can include a set of parameters 316 thatmathematically represent the portion of the lumen between the points 308and 310. The output parameters can be provided and stored to a file,printer or other media. The parameters can be provided in a form thatcan be employed by standard engineering tools, such as for furtheranalysis including simulation, generation of a three-dimensional modeland/or manufacture of an endovascular stent.

Computer system 200 may operated a networked environment using logicalconnections to one or more remote computers, such as remote computer228. Remote computer 228 may be a workstation, computer system, router,peer device, or other common network node, and typically includes manyor all the elements described relative to computer system 200. Thelogical connections, schematically indicated at 230, can include a localarea network (LAN) and a wide area network (WAN).

When used in a LAN networking environment, computer system 200 can beconnected to the local network through a network interface or adapter232. When used in a WAN networking environment, computer system 200 caninclude a modem, or can be connected to a communications server on theLAN. The modem, which may be internal or external, can be connected tosystem bus 203 via an appropriate port interface. In a networkedenvironment, application programs 216 or program data 218 depictedrelative to computer system 200, of portions thereof, may be stored in aremote memory storage device 240.

In view of the structural and functional features described above,certain methods will be better appreciated with reference to FIG. 17. Itis to be understood and appreciated that the illustrated actions, inother embodiments, may occur in different orders or concurrently withother actions. Moreover, not all features illustrated in FIG. 17 may berequired to implement a method. It is to be further understood that thefollowing methodology can be implemented in hardware (e.g., one or moreprocessors, such as in a computer or computer system), software (e.g.,stored in a computer readable medium or as executable instructionsrunning on one or more processors), or as a combination of hardware andsoftware.

FIG. 17 depicts an example of a basic method 350 that can be utilized toidentify a centerline of a tubular structure according to an aspect ofthe invention. The method 350 is particularly well suited foridentifying a centerline of a tortuous curved path. Examples of suchcurved paths occur frequently in arterial lumen, the colon, othervascular structures and vessels. The method begins at 360 in which anedge detected data set of voxels is provided to characterize a boundaryof a tubular structure. Various methods and approaches can be utilizedto process raw image data and to identify boundary of the correspondingtubular structure.

At 370, a distance transform is computed for the edge detected data set.The distance transform computed at 30 essentially converts the Booleanimage provided by the edge detected voxel data set into a gray-levelimage for voxel values identified the distance a given element is fromone of the border elements. Those skilled in the art will understand andappreciate various distance transformations (e.g., the Manhattan orEuclidean distance metrics) that can be utilized. At 380, a gradientfield of the resulting distance transformation is computed. The gradientfield provides a gradient vector field that can be numericallyapproximated due to the discrete nature of the information in thedistance transform gradient data set.

At 390, a centerline is identified based on the derivative of thegradient field. The derivative computation can be performed as a scalarderivative of the vector field using a neighborwise dot product. Thecomputed derivative can be utilized (e.g., via a thresholding procedure)to identify voxels where the gradient of the distance transform changesrapidly, as these voxels define the centerline.

The method 330 can be repeated for each set of image data such as maycorrespond to images of the tubular structure at different instances oftime. For example, the image data set can correspond to a 4-D CT scan inwhich a plurality of different image sets are required for the tubularstructure over a period of time. The method 350 can be repeated for eachtime slice so that the centerline can be identified for the differentconfigurations or conditions that the tubular structure may exist inover the period of time in which the images are acquired.

At 400, a surface model is computed based on die identified centerline.As described herein, the surface model can be determined by firstcomputing an analytical expression for the identified centerline andthen computing the surface model based on the centerline and a segmenteddata set for the tubular structure. Those skilled in the art willunderstand and appreciate various approaches that can be employed tocompute a corresponding surface model.

The particular mathematical model used to describe the geometry providesits own advantages. The list of equations and parameters which fullydescribes the shape of the arterial lumen is both compact andappropriate for the purpose of describing a bifurcating lumen. Ratherthan consisting of a huge grid of numbers occupying hundreds ofmegabytes, as a DICOM image does, it consists of a small set of numbersoccupying mere kilobytes. Further, the structure of the numbers actuallycontains meaningful information about the underlying geometry. Thepotential utility of such a representation is great when one considersthe ease with which it can be transmitted, shared, and stored.

The precision, accuracy, comprehensibility, and conciseness of thismodel make available a multitude of directions for future work. Inaddition to surgery planning, this geometric analysis can be used fordiagnostic purposes. For example, because it inherently quantifies thediameter of the lumen, it is well-suited for identifying aneurysmal orstenosed vessels. Additionally, an implantable device, such as a stentor other structure, can be dimensioned and configured as a function of amathematical model produced according to methods described herein. Themathematical model also can be utilized intraoperatively, such as byproviding a visual representation that can be superimposed or fused withreal time imaging data. As a further example, the shape of a cathetercan be computed as a function of the analytical model. Thus, manual orautomatic means can be employed to configure a catheter or otherdelivery device to facilitate travel through a lumen. For instance, arobotic system can change the shape of a distal end portion of asteerable catheter as a function of the model, as well as advance thedistal end of the catheter intra-lumenally along a desired path, whichpath can also be determined as a function of the model.

The advent of 4-DCT scans presents a great opportunity for thoroughgeometric analysis. The ability to visualize the movement of anatomy asthe cardiac cycle progresses allows for immensely greater understandingof tissue than is possible with only 3-D scans. For example, there isevidence that the material properties of the aortic wall can predict thelikelihood of a dissection in patients predisposed to such an event. Ahigh-resolution 4-D CT scan combined with a thorough geometric analysiscan yield more precise quantification of geometric change than ispossible with lower-resolution or lower-dimensional imaging techniques.

FIG. 18 depicts an example of a fusion system 500 that can combine agraphical representation of a model with other image data to provide afused image. The system 500 can import or otherwise be provided modeldata 502, such as data corresponding to a mathematical model generatedaccording to an aspect of the invention. For example, the model data 502can include a surface model of a length of a patient's vasculature orother anatomic structure. The model can be generated from a prior 3Dimage acquired for a given patient. As described herein, the model canbe generated based on data acquired from a variety of one or moreimaging modalities. The model data 502 can correspond to a single static3D model. Alternatively, the model data 502 can be constructed as a 4Dmodel from a plurality of images. Such a 4D model can include a separatemodel data set for each of plurality of phases of an image acquisitionprocess. The phases, for instance, can be a set of images gated tophysiological condition of the patient, such as can include gating tothe patient's cardiac cycle (e.g., ECG gating), the patient'srespiration or may include both cardiac and respiratory gating. In thisway, 4D model data 502 can represent deformation of the modeledanatomical structure over a period of time. Additionally, as describedherein, one or more anatomical markers or landmarks can be included inor be associated with the model data to facilitate registration of themodel with other image data as described herein.

FIG. 19 depicts an example of an image 600 that includes anatomicallandmarks 602 and 604 that can be associated with an analytical model tofacilitate registration of the model, as described herein. FIG. 20 isanother image illustrating a wire frame representation for a surfacemodel 610 of a portion of a descending aorta, such as can be generatedaccording to an aspect of the invention. Also shown in FIG. 20 are theanatomical landmarks 602 and 604 such as can be acquired and associatedwith the model. As described herein, the landmarks 612 can be utilizedto facilitate registration of a graphical representation of the modelinto another image set of the patient's anatomy.

The system 300 includes an imaging system 504 that is configured toacquire images of the anatomy of a patient 506 according to one or moreimaging modality. By way of example, the imaging system 504 may beimplemented as a CT device (e.g., a cardiac CT system), a fluoroscopicimaging system, a magnetic resonance imaging (MRI) device, a positronemission tomography (PET) device or a combination of two or moremodalities (e.g., PET/CT system). In one embodiment, the imaging system504 can be implemented as an intraoperative imaging system that includesa C-arm on which an X-ray source and a radiation detector are mounted.In such an imaging device, the field of examination of the patient 506is located in an isocenter of the C-arm for generating images of thepatient's anatomical features within the isocenter.

The imaging system 504 generates an image data set 508. The image dataset 508 can represent one or more two-dimensional images of thepatient's 506 anatomy or one or more 3D images of the patient's anatomy.For instance, two-dimensional images can be processed to generate acorresponding 3D image. Alternatively, a series of 3D images can beacquired for the patient to provide a corresponding 4D image data set.For instance, the 4D image data set can include a plurality of phasesacquired over a period of time, such by cardiac gating and/orrespiratory gating the image acquisition process for the patient 506. Itis to be understood that the particular type of gating utilized toacquire the image data set 508 can be the same as or be consistent withthe gating utilized in the image acquisition process for obtaining theimage data from which the model data 502 has been generated. In thisway, for 4D scenario, the phases of the model data 502 can align withrespective phases of the image data set 508 acquired by the imagingsystem 504.

FIG. 20 depicts one example of an image 620 that can be acquired byfluoroscopy for a given patient into which the model is to be fused. Theimage 620 includes anatomy of interest (e.g., the aorta) as well assurrounding anatomical features, including the anatomical landmarks thathave been associated with the model.

Referring back to FIG. 18, the system 500 also includes an image fusionengine 510 that is programmed to merge the model represented by themodel data 502 into an image represented by the image data to provide acorresponding fused image data set 514. However, as described herein,the model data 502 is a mathematical model, such as a surface model thatmathematically defines a surface of an anatomical structure of thepatient 506. Thus, the system 500 can include a converter 512 mat isprogrammed (if necessary) to convert the model data 502 into a formatthat is compatible with the image data set 508. As one example, theimage data set 508 can be stored according to the DICOM (Digital Imagingand Communications in Medicine) standard, which has been developed andsponsored by the American College of Radiology and the NationalElectrical Manufacturers Association. The converter 512 thus can link orotherwise associate the model (defined by the model data 502) or anumerical representation of the model with the image date set 508. Whilein the example of FIG. 18, the converter is depicted as part of thesystem 500, it will be appreciated that the converter can be implementedseparately, such as by converting the model to an appropriate formatconcurrently with the model being generated. The converter 512 furthermay be programmed to convert the model data 502 to any number of one ormore formats to enable substantially seamless integration of the modeland the image being acquired.

The image fusion engine 510 generates the fused image data set 514 thatincludes a graphical representation of the model superimposed on agraphical representation of the image defined by the image data set 508.The image fusion engine 510 can perform appropriate/scaling andregistration of the model into the image by utilizing the anatomicalmarkers or landmarks identified for each of the model data 502 and theimage data set 508. Those skilled in the art will appreciate anappropriate set of one or more image features that can be selected asmarkers or landmarks for registering the model into the newly acquiredimage. Such features, for example, can include anatomical structures,boundaries of structures and the like. Additionally, for the 4D example,it will be appreciated that each phase of the model and the image can bealigned matched by employing anatomical markers provided for each suchphase, which may be the same or different for each respective phase. Theresulting fused image data set further may be provided to a display 516,which can provide intraoperative guidance.

FIG. 22 depicts an example of a fused image 630 in which the wire framerepresentation of the surface model 610 (FIG. 20) has been registeredinto the image 620 (FIG. 21) acquired for the patient. The registrationof the model 610 and the image of the patient anatomy is facilitatedbased on the common identifiable anatomical landmarks 612 (FIG. 20) inthe respective images. While the fusion process has been described as anautomated process running on a computer, it will be appreciated that theregistration may also be performed manually according to an aspect ofthe invention.

FIG. 23 depicts an example of a system 700 that is programmed andconfigured to control a steerable catheter system 702 based on ananalytical expression of a model determined according to an aspect ofthe invention. The system 700 can include many of the same types ofcomponents as the fusion system 500 of FIG. 18. Accordingly, additionalinformation regarding these common features and components can beobtained with reference back to the description of FIG. 18.

Briefly stated, the system 700 can import or otherwise be provided modeldata 704, such as data corresponding to a mathematical model accordingto an aspect of the invention. For example, the model data 502 caninclude a surface model of a length of a patient's vasculature or otheranatomic structure. Additionally or alternatively, the model data canparameterize a centerline for the patient's vasculature or otheranatomic structure of interest. The model data 704 can correspond to asingle static 3D model or a 4D model from a plurality of images.Additionally, as described herein, one or more anatomical markers oflandmarks can be included in or be associated with the model data tofacilitate registration of the model with other image data as describedherein.

The system 500 includes an imaging system 706 that is configured toacquire images of the anatomy of a patient 708 according to one or moreimaging modality, such as including any modality described herein. Theimaging system 706 generates an image data set 710, which can correspondto a 2-D or 3-D of 4-D visualization of the patient's anatomy, includingat least a portion of the anatomy for which the model has beengenerated. Typically the model data 704 will be constructed a priori,although as processor speeds continue to increase, it is contemplatedmat the model data can be generated in a run time operation based on theimage data set 710 (e.g., which can be acquired intraoperatively).

The system 700 also includes a fusion engine 712 that is programmed tomerge the model represented by the model data 704 with ah imagerepresented by the image data 710 to provide a corresponding fused imagedata set 716. As described herein, the model data 704 corresponds to amathematical model, such as a surface model that mathematically definesa surface of an anatomical structure of the patient 708 and/or acenterline model that defines a centerline of the anatomical structure.Thus, the system 700 may include a converter 714 that is programmed toconvert the model data 704 into a format that is compatible with theimage data set 710. The image fusion engine 712 generates the fusedimage data set 716 that includes a graphical representation of the modelsuperimposed on a graphical representation of the image defined by theimage data set 716. The resulting fused image data set further may beprovided to a display 718, which can provide intraoperative guidance.

The system 700 also includes a controller 720 that is programmed tocontrol the steerable catheter system 702. The control that is providedby the system can vary according to the type of procedure and equipmentavailable. For instance, the controller can provide for manual control(e.g., based on the display of a graphical representation of a fusedimage). Additionally, or alternatively, the controller 720 can providefor robotically assisted manual control (e.g., some amount of manualcontrol of the steerable catheter is required) or it can provide forfully automatic robotic control. The controller 720 can be implementedas a computer that includes memory programmed with instructions, whichwhen executed by one or more processors perform one or more methods forcontrolling the catheter system 702.

For example, the controller 720 can implement one or more methods(depicted as including a position calculator 722, a trajectorycalculator 726, shape control 728 and actuator control 730) that employsan iterative process to direct distal tip to the desired position,responsive to position, information (e.g., generated by aposition-measurement system 732 and/or by the fused image data set 716)at each iteration. By continuously checking the location of distal tipand appropriately driving the control mechanisms to adjust the shape andposition of the distal end portion of the catheter 724, the distal endportion can be controlled to a substantially precise location andconfiguration, regardless of the particular structure of catheter ofcharacteristics of the tissue surrounding catheter at any given time.

The position calculator 722 is programmed to compute the position of acatheter, indicated schematically at 724, within the patient 708. Theposition calculator 722 can also determine a configuration of the distalend portion of the catheter 724. The configuration information can bedetermined based on the image of the catheter and/or based on controlinformation provided associated controls or feedback from the cathetersystem 702. The position calculator 722 can compute the position andconfiguration of the catheter 724 based on one or both of the image dataset 710 and the fused image data set 716. Additionally or alternatively,the system 700 can include a position measurement system 732 that isconfigured to provide an indication of position for the catheter withinthe patient's body 708. Examples of the position measurement systeminclude placing a sensor at the distal end of the electrode with anelectromagnetic measurement system placed near the body to determine theposition of the catheter in the patient 708. Those skilled in the artwill understand and appreciate other types of position measurementsystems that can be utilized to provide an indication of position andconfiguration of the distal end portion of the catheter 724.

The trajectory calculator 726 is programmed to determine a desiredtrajectory for advancing the catheter 724 in the patient. For example, adesired trajectory can be determined as corresponding to a path definedby a centerline that is represented by the model data 704. Thecontroller 720 also includes shape control 728 and actuator control 730that collectively are programmed to control the shape and position ofthe catheter 724. For instance, the shape control 728 can be programmedto send control signals to the steerable catheter to cause theconfiguration of the distal end portion to match a particularconfiguration, such as determined by the trajectory calculator 726. Theparticular manner of control and the types of shapes (e.g., radius ofcurvature) will generally vary according to the type of steerablecatheter 724. Thus, the shape control 728 can be programmed to achievedeflection of the distal end portion of the catheter 724 relative to itslongitudinal axis ‘A’.

The trajectory determined by the trajectory calculator 726 can includeone of a main trunk and any number of one or more branches of a tubularstructure, such as including the aorta or other generally tubularanatomical structures. The centerline represented by the model data 704can be utilized by the trajectory calculator to provide one possibletrajectory. The particular trajectory can vary according to thedestination site of the catheter, which information can be entered intothe controller via a user interface (not shown). While the shape andactuator control functions 728 and 730 are depicted as separate methodsof the controller 720, it will be understood that single control methodcan be employed as means for changing the configuration and foradjusting the position distal end portion of the catheter 724.

As described herein, the centerline for a multi-branched structure canbe truncated at the branches, such that a continuous trajectory may notexist in the model data 704 for a trajectory that includes multiplebranches. Accordingly, the trajectory calculator 726 can be programmedto compute a curved path as a function of two adjacent centerlines asrepresented by the model data 704, such as a function of the centerlinecomputed for a main trunk and the centerline computed for acorresponding branch. The trajectory calculator 726 can compute theresulting trajectory as including gradual-curved path that interconnectsthe two centerlines. To determine such a curved path, the trajectorycalculator 726 can identify end points on the centerlines that arespaced axially apart from the location where the centerline truncates(e.g., by moving along each centerline away from the adjacent branchcenterline). This enables the trajectory calculator to determine a moregradual curve that can be more easily imparted to the catheter by theshape control 728.

The shape control 728 thus can be programmed to cause the distal endportion of the catheter 724 to have a configuration that substantiallymatches the computed trajectory that includes multiple centerlines andthe curved path that interconnects the centerlines. The shape control728 can further vary configuration can further vary depending theposition of the distal end of the catheter (determined by the positioncalculator) which position will vary according to axial movement of thecatheter effected by the actuator control 730. Thus, as the actuatorcontrol causes the distal end of the catheter to advance axially along adetermined trajectory, the model data 704 provides substantial real timefeedback that can be utilized by the shape control 728 to adjust dieshape of the distal end portion of the catheter 724. It will beappreciated that manual override can be implemented to further adjustthe shape of the catheter and or to adjust the axial position of thedistal end portion.

While the example of FIG. 23 is described with respect to a steerablecatheter system 702, it will be understood that the system 700 isapplicable to virtually any types of steerable, flexible medicaldevices, such as guide wires, introducer, sheaths, guiding catheters, orany similar medical device. Those skilled in the art will understand andappreciate various types and configurations of steerable catheters andother flexible and steerable medical devices that can be utilized in thecatheter system 702.

As one example, the catheter system can include a plurality of pullerwires disposed about the circumference of the catheter at a plurality ofaxial positions and extend along its length, typically passing throughrespective lumens. The distal ends of the puller wires can be attachedat respective points proximal to a distal end of the catheter (e.g., ataxially and circumferentially spaced apart locations), and the proximalends of the wires are coupled to respective motors or other actuators.The motors are able to tense and relax the respective puller wires tomanipulate (e.g., cause deflection of) the distal end of the catheter toa desired configuration. Alternatively, catheter system 702 can employdifferent types of steering mechanisms, including, for example, asteering mechanism that utilizes shape memory alloys (SMAs),electroactive polymers (EAPs), and/or ionic polymer metal composites(TPMCs). Some examples of existing steerable medical devices that can beimplemented, in whole or in part, as the catheter system 702, aredisclosed in U.S. Pat. Nos. 6,997,870 and 7,077,823, U.S. PatentPublication Nos. 2007/0197896 and 2007/0100235 and International PatentPublication No. WO 2006/119,495.

For instance, U.S. Pat. No. 6,997,870 discloses a type of guide catheteris provided in which electroactive polymer actuators are integrated intothe guide catheter structure. A control unit is coupled to actuators andsends control signals to the actuators. Based upon the control signalsreceived from the control unit the actuators change the shape of a guidecatheter portion.

U.S. Patent Publication No. 2007/0197896 discloses using a roboticallycontrolled guide instrument coupled to an instrument drive assembly. Auser interface of a master controller is utilized to actuate the driveassembly and thereby position a distal portion of the guide instrumentat a site in a patient's body. The location of the guide instrument maybe determined from real-time image data of the patient's body or fromlocalization data obtaining from one or more sensors carried on theguide instrument.

U.S. Patent Publication No. 2007/0100235 discloses steerable catheterdevices and methods of using articulating catheter devices. Thesteerable catheter imparts bending at a distal end of an elongatedcatheter by providing a change in internal fluid pressure.

U.S. Pat. No. 7,077,823 discloses a steerable catheter that has twopuller wires, which are respectively coupled to two movable elements ina control handle, whereby displacement of movable element coupled tofirst puller wire causes deflection of catheter tip.

Each of these above-described patents and patent publication (U.S. Pat.Nos. 6,997,870 and 7,077,823, U.S. Patent Publication Nos. 2007/0197896and 2007/0100235 and International Patent Publication No. WO2006/119,495) is incorporated herein by reference. Based on theteachings contained in this document and any document indicated as beingincorporated by reference, one skilled in the art will understand howthe examples in the above-incorporated patents and patent publicationsmay be modified to utilize the model data to control positioning acatheter.

FIG. 24 depicts an example of a graphical depiction of a tubularstructure 800 for demonstrating how a trajectory can be computed, suchas by the trajectory calculator 726 in the system 700 of FIG. 23. In theexample of FIG. 24, the tubular structure 800 includes a main branch 802and a plurality of branches 804, 806 and 808. The main branch 802includes a centerline 810 that has been computed and defined by a modelaccording to an aspect of the invention. Each of the branches 804, 806and 808 also includes a respective centerline 812, 814 and 816 computedin a similar manner as described herein. Thus, each of the branchcenterlines 812, 814 and 816 is truncated from the main branchcenterline 810. The main branch centerline can also be truncated at theregion where the branches 806 and 810 extend or, alternatively, the mainbranch centerline can be interpolated at such region, as indicated atdotted line 818.

By way of example, a curved trajectory 820 can be computed as extendfrom the main branch 802 into the lateral branch 806 as a function ofthe centerlines 810 and 814. To improve the gradual nature of the curvedpath trajectory 820 interconnecting the centerlines 810 and 814, thepath can walk backward along the centerline 810 a distance, indicated at822, to define a starting point 824 for the computed trajectory on thecenterline 810 that is spaced axially apart from the point 826 where thecenterline 810 ends. It will be understood that trajectories can becomputed similarly to interconnect the centerlines for any two adjacentbranches in the structure 800. Since the centerlines 810 and 814 aremathematical models, the resulting interconnecting.

What have been described above are examples of the invention. It is, ofcourse, not possible to describe every conceivable combination ofcomponents or methodologies for purposes of describing the invention,but one of ordinary skill in the art will recognize that many furthercombinations and permutations of the invention are possible.Accordingly, the invention is intended to embrace all such alterations,modifications, and variations that fall within the scope of thisdescription, including the appended claims.

What is claimed is:
 1. A non-transitory computer-readable mediumincluding instructions executable by a processor to perform a method,the method comprising: providing an edge-detected data set of thatrepresents a surface boundary of a three-dimensional generally tubularstructure according to a three-dimensional voxel data set for thetubular structure; computing a gradient vector field of a distancetransformation for the edge-detected data set; computing a scalarderivative of each voxel in the gradient vector field relative toadjacent voxels to provide a derivative field for the voxels in theedge-detected data set, wherein the derivative field identifies a rateat which each voxel is changing direction; thresholding the derivativefield of the voxels to identify a voxel data set that includes aplurality of contiguous voxels where the gradient vector field changesrapidly, according to the computed derivative, the plurality ofcontiguous voxels defining a continuous centerline of the tubularstructure, the identified voxel data set being stored in memory todefine the centerline of the tubular structure; and generating a modelthat parameterizes the centerline of the tubular structure in athree-dimensional coordinate system based on the voxel data set thatincludes the plurality of contiguous voxels.
 2. The medium of claim 1,wherein the scalar derivative is performed using a neighborwise dotproduct function to generate the scalar derivative of the gradientvector field.
 3. The medium of claim 1, wherein the method furthercomprises computing a distance transform of the edge-defected data set,the gradient vector field being computed being computed based on thecomputed distance transform.
 4. The medium of claim 3, wherein thecomputing of the distance transform further comprises computing athree-dimensional distance transformation for the edge-detected data setthat satisfies the Eikonal equation.
 5. The medium of claim 1, whereinthe model comprises extracting geometric knots to produce acorresponding spline model of the continuous centerline of the tubularstructure.
 6. The medium of claim 1, wherein the method furthercomprises computing another model that parameterizes a surface of thetubular structure as a function of the expression that parameterizes thecontinuous centerline of the tubular structure.
 7. The medium of claim6, wherein the method further comprises computing a plurality oftwo-dimensional slices, each of the plurality of two-dimensional sliceshaving a local coordinate system aligned relative to the continuouscenterline of the tubular structure and including points defined by aboundary of the surface of the tubular structure for the respectiveslice.
 8. The medium of claim 7, wherein the computing of the pluralityof two-dimensional slices further comprises marching radially outwardfrom the continuous centerline of the tubular anatomical structure toidentify a set of geometric knots for each slice that define theboundary for the surface of the tubular anatomical structure.
 9. Themedium of claim 7, wherein, if at least two of the plurality oftwo-dimensional slices intersect, at least one of the intersectingslices is relocated along the continuous centerline of the tubularstructure to eliminate such intersection.
 10. The medium of claim 7,further comprising interpolating between the plurality oftwo-dimensional slices to construct a graphical representation of thesurface of the tubular structure.
 11. The medium of claim 6, wherein themodel that parameterizes the surface of the tubular structure defines asurface model for the tubular structure, the method further comprising:acquiring an image data set for a portion of a patient's anatomy; andsuperimposing a representation of the surface model onto a graphicalrepresentation of the portion of the patient's anatomy.
 12. The mediumof claim 11, wherein prior to the superimposing, the method furthercomprises converting the surface model to a format that is consistentwith a format of the image data set.
 13. The medium of claim 1, whereinthe tubular structure further comprises a main branch and at least oneother branch that intersects with the main branch, the thresholding ofthe derivative field being performed to identify the contiguous set ofvoxels that defines a respective continuous centerline of the mainbranch and at least one other contiguous set of voxels that defines arespective continuous centerline of the at least one other branch, themodel that parameterizes the centerline of the tubular structurecomprising a first centerline portion that parameterizes a firstcontinuous centerline for the main branch and a second centerlineportion that parameterizes a second continuous centerline for the atleast one other branch.
 14. The medium of claim 13, wherein the methodfurther comprises computing a curved path as a function of the firstcenterline portion and the second centerline portion, the curved pathrepresenting a path that interconnects the continuous centerline of themain branch with the continuous centerline of the at least one branch.15. The medium of claim 14, wherein the method further comprisescontrolling a shape of a distal end portion of a steerable catheter as afunction of the curved path.
 16. The medium of claim 13, wherein tubularstructure comprises a length of a three-dimensional anatomical tubularstructure.
 17. The medium of claim 1, wherein the method furthercomprises: computing a trajectory through the tubular structure based atleast in part on the model that parameterizes the continuous centerlineof the tubular structure, the trajectory parameterizing a curved paththrough the tubular structure; and controlling a steerable flexiblemedical device according to the computed trajectory.
 18. The medium ofclaim 1, wherein the method further comprises: employing athree-dimensional imaging modality to acquire the three-dimensionalvoxel data set; performing preprocessing of the three-dimensional voxeldata set to provide a corresponding segmented voxel data set for thetubular structure; and detecting a border of the corresponding segmentedvoxel data set to provide the edge-detected data set.
 19. The medium ofclaim 1, computing an analytical model that parameterizes a surface ofthe tubular structure based at least in part on the model for thecenterline of the tubular structure, wherein the edge-detected data setis provided for each of a plurality of different instances in time,wherein the computing of the gradient vector field, the computing of thederivative of each voxel in the gradient vector field and thethresholding the derivative field are repeated for each of the differentinstances in time to identify a respective centerline for each of thetime instances, and the analytical model representing deformation of thetubular structure over time; and superimposing a graphicalrepresentation of the tubular structure, generated from the analyticalmodel, with a graphical representation of image data acquired foranatomy of a patient that includes the tubular structure.
 20. The mediumof claim 1, wherein the method further comprises: determining a centerof mass for a subset of the contiguous set of the identified voxelsalong the tubular structure; defining corresponding geometric knotsalong the centerline based on the determined center of mass; andgenerating the model that parameterizes the centerline of the tubularstructure as a function of the geometric knots.
 21. An image processingsystem comprising: a distance transform executing instructions tocompute a distance transformation for an edge-detected data set, theedge-detected data set including voxels that represent athree-dimensional volume that includes a structure of interest; agradient operator programmed to compute a gradient vector field of thedistance transformation; a derivative component programmed to compute ascalar derivative of the gradient vector field and provide a derivativefield, wherein the derivative field identifies a rate at which eachvoxel is changing direction; and a centerline extractor programmed tothreshold the derivative field to identify a voxel data set thatincludes a contiguous set of voxels based on where the derivative of thegradient vector field changes rapidly, the contiguous set of voxels inthe identified voxel data set defining a continuous centerline of thestructure of interest; and a centerline model generator programmed togenerate a model that parameterizes the continuous centerline of thetubular structure in a three-dimensional coordinate system based on thevoxel data set that includes the contiguous set of voxels.
 22. Thesystem of claim 21, wherein the derivative of the gradient vector fieldcomprises a scalar derivative of the gradient vector field.
 23. Thesystem of claim 21, further comprising a surface model generatorprogrammed to compute another model for a surface of the structure ofinterest based at least in part on the model for the continuouscenterline of the structure of interest.
 24. The system of claim 23,wherein the model for a surface of the structure of interest is asurface model, the system further comprising: a converter programmed toconvert the surface model to an image format consistent with an imagedata set acquired by an intraoperative imaging system; and an imagefusion engine programmed to superimpose a graphical representation ofthe surface model with a graphical representation the image data set.25. The system of claim 21, wherein the structure of interest furthercomprises a main generally tubular branch and at least one othergenerally tubular branch that intersects with the main generally tubularbranch, the thresholding of the derivative field being performed by thecenterline extractor to identify the contiguous set of voxels thatdefines a respective continuous centerline of the main branch and atleast one other contiguous set of voxels that defines a respectivecontinuous centerline of the at least one other branch, the centerlinemodel generator computing the model for the continuous centerline toinclude a first centerline portion that defines a first continuouscenterline of the main generally tubular branch and a second centerlineportion that defines a second continuous centerline of the at least oneother generally tubular branch.
 26. The system of claim 25, furthercomprising a trajectory calculator programmed to compute a curved pathas a function of the first centerline portion and the second centerlineportion, the curved path representing a path that interconnects thecontinuous centerline of the main generally tubular branch with thecontinuous centerline of the at least one generally tubular branch. 27.The system of claim 26 in combination with a steerable catheter system,the combination further comprising: a steerable catheter comprising anelongate body that terminates in a distal end portion; and a controllerprogrammed to cause the distal end portion of the steerable catheter tobe configured as a function of the curved path.
 28. The system of claim21, further comprising an edge detector programmed to detect a border ofthe structure of interest from a segmented voxel data set thatrepresents at least the structure of interest.
 29. The system of claim21, wherein the structure of interest comprises a three-dimensionalanatomical tubular structure.
 30. An image processing system comprising:means for computing a distance transformation to identify a relativedistance of image elements relative to image elements located at aborder determined for a three-dimensional structure of interest; meansfor computing a gradient vector field of the distance transformation;means for computing a scalar derivative of the gradient vector field toproduce a derivative field, wherein the derivative field identifies arate at which each voxel is changing direction; means for thresholdingthe derivative field to identify a voxel data set that includes aplurality of contiguous voxels along the structure of interest based onthe derivative of the gradient vector field, the plurality of contiguousvoxels defining a continuous centerline of the three-dimensionalstructure of interest; and means for determining a model thatparameterizes the continuous centerline of the three-dimensionalstructure of interest.
 31. The system of claim 30, wherein thederivative of the gradient vector field comprises a scalar derivative ofthe gradient vector field.
 32. The system of claim 30 furthercomprising: means for computing another model that parameterizes asurface of the three-dimensional structure of interest based at least inpart on the model for the continuous centerline of the three-dimensionalstructure of interest; and means for superimposing a graphicalrepresentation of the three-dimensional structure of interest, generatedfrom the model that parameterizes the surface model, with a graphicalrepresentation of image data acquired for anatomy of a patient thatincludes the three-dimensional structure of interest.
 33. The system ofclaim 30, wherein the three-dimensional structure of interest furthercomprises an anatomical structure comprising a main generally tubularbranch and at least one other generally tubular branch that intersectswith the main generally tubular branch, the means for thresholding ofthe derivative field further identifying the contiguous set of voxelsthat defines a respective continuous centerline of the main branch andat least one other contiguous set of voxels that defines a respectivecontinuous centerline of the at least one other branch, the model thatparameterizes the continuous centerline being computed to provide afirst centerline portion that parameterizes a continuous centerline ofthe main generally tubular branch and a second centerline portion thatparameterizes a continuous centerline of the at least one othergenerally tubular branch.
 34. The system of claim 33, further comprisingmeans for computing a trajectory as a function of the first centerlineportion and the second centerline portion, the trajectory parameterizinga curved path that interconnects the continuous centerline of the maingenerally tubular branch with the continuous centerline of the at leastone generally tubular branch.